Convert Quantized Hall Resistances to Abohms
Quantized Hall Resistance (R_K) to Abohm (abΩ) electric resistance conversion — enter any value below to get an instant result, or use the table for common values.
Results from this calculator are estimates provided for general informational purposes only, based on formulas, rates, and standards commonly accepted as of 2026. Figures may differ slightly from other calculators or professional sources due to rounding methods, differing assumptions, or regional regulations, and rules may change over time. Always consult a qualified professional — such as a financial advisor, healthcare provider, or other relevant specialist — before making decisions based on these results.
Result
1 R_K = 2.58128E+13 abΩ
1 Quantized Hall Resistance = 2.58128E+13 Abohms
1 Abohm = 3.87405E-14 Quantized Hall Resistances
1 R_K in every supported unit
Conversion chart: Quantized Hall Resistance to Abohms
Conversion table
| Quantized Hall Resistance (R_K) | Abohm (abΩ) |
|---|---|
| 0.01 R_K | 2.58128E+11 abΩ |
| 0.1 R_K | 2.58128E+12 abΩ |
| 1 R_K | 2.58128E+13 abΩ |
| 2 R_K | 5.16256E+13 abΩ |
| 3 R_K | 7.74384E+13 abΩ |
| 5 R_K | 1.29064E+14 abΩ |
| 10 R_K | 2.58128E+14 abΩ |
| 20 R_K | 5.16256E+14 abΩ |
| 50 R_K | 1.29064E+15 abΩ |
| 100 R_K | 2.58128E+15 abΩ |
| 1000 R_K | 2.58128E+16 abΩ |
Quantized Hall Resistance (R_K)
Definition: A fundamental resistance quantum, R_K = h / e² (Planck's constant divided by the square of the elementary charge), that appears as the quantized plateaus of Hall resistance in the quantum Hall effect.
History: Discovered by Klaus von Klitzing in 1980 — work for which he received the 1985 Nobel Prize in Physics — the effect proved so precisely reproducible that the international metrology community adopted a fixed conventional value, R_K-90 = 25,812.807 ohms, as the worldwide resistance standard starting in 1990.
Current use: Still used by national metrology institutes to realize and calibrate the ohm with extraordinary precision, now tied to exact values of Planck's constant and the elementary charge under the SI's 2019 redefinition.
Abohm (abΩ)
Definition: The base unit of electric resistance in the CGS electromagnetic (EMU) system, equal to exactly one billionth of an ohm.
History: Part of the family of "ab-" prefixed CGS-EMU units — alongside abvolt, abampere, and abhenry — developed by 19th-century physicists including Wilhelm Weber, before the SI's ampere-based electromagnetic convention became the international standard.
Current use: Rarely used today outside historical physics literature and legacy Gaussian-unit papers on electromagnetism, where resistances were traditionally expressed in abohms.
Supported Units
| Unit | Symbol | In Ohm |
|---|---|---|
| Ohm | Ω | 1 Ω |
| Kiloohm | kΩ | 1000 Ω |
| Megohm | MΩ | 1000000 Ω |
| Milliohm | mΩ | 0.001 Ω |
| Microhm | μΩ | 1E-06 Ω |
| Volt/Ampere | V/A | 1 Ω |
| Reciprocal Siemens | 1/S | 1 Ω |
| Abohm | abΩ | 1E-09 Ω |
| EMU of Resistance | EMU | 1E-09 Ω |
| Statohm | statΩ | 8.98755E+11 Ω |
| ESU of Resistance | ESU | 8.98755E+11 Ω |
| Quantized Hall Resistance | R_K | 25812.807 Ω |
About These Parameters
- Value
- The electric resistance value you want to convert, expressed in the "From" unit. Accepts decimals, and can represent anything from a microhm-scale connector contact resistance to a megohm-scale insulation-resistance reading.
- From Unit
- The unit your input value is currently measured in — a resistor's printed ohm or kiloohm rating, a megohmmeter's insulation reading, or an older figure quoted in a CGS unit like the abohm or statohm.
- To Unit
- The unit you want the result converted into. Use the swap button to flip From and To instantly, which is handy when moving between a datasheet's units and the ones used in your own calculations.
How Electric Resistance Conversion Works
The Formula
Every unit here is defined by a fixed multiplier relative to the ohm. To convert a value from one unit to another:
result = value × (factor of "From" unit ÷ factor of "To" unit)
For Quantized Hall Resistance → Abohm: multiply by 2.58128E+13. For example, 1 R_K × 2.58128E+13 = 2.58128E+13 abΩ.
Ohm's Law and the Origin of the Ohm
Georg Simon Ohm published his now-famous law in 1827, showing that the current through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance — a relationship so fundamental that essentially every electrical calculation traces back to it. At the time his work was met with skepticism and largely ignored by the German physics establishment; recognition came only later, and it wasn't until the International Electrical Congress of 1881 that "ohm" was formally adopted as the name of the resistance unit, defined so that one ohm is the resistance that lets one ampere flow when one volt is applied. Every SI multiple on this page — from milliohm up through megohm — is simply that same unit scaled by a power of ten for convenience.
Why CGS Resistance Units Still Appear
Before the SI system unified electrical units around the ampere, 19th-century physicists worked with two parallel centimeter-gram-second (CGS) systems: the electromagnetic (EMU) system, which gave us the abohm, and the electrostatic (ESU) system, which gave us the statohm — a unit so much larger than the ohm that it differs by a factor tied to the speed of light. Both systems were mathematically elegant for theoretical physics but impractical for engineering, which is why they were eventually superseded by the ampere-based SI units used almost everywhere today. They still turn up when reading historical electromagnetism papers or textbooks written in Gaussian units.
Example
An electric resistance of 1 R_K equals 2.58128E+13 abΩ. For scale, a typical carbon-film resistor might be rated between 100 ohms and a few megohms, a copper shunt used for current sensing might measure just a few milliohms, and a healthy insulation-resistance test on household wiring should read well into the megohms.
Frequently Asked Questions
How many Abohms are in 1 Quantized Hall Resistance?
1 Quantized Hall Resistance (R_K) equals exactly 2.58128E+13 Abohms (abΩ).
What's the difference between resistance and resistivity?
Resistance (measured in ohms) depends on a specific object's shape — its length and cross-sectional area — as well as the material it's made of. Resistivity (measured in ohm-meters) is a pure material property that stays the same regardless of the object's dimensions. Two wires of the same copper have the same resistivity, but a longer or thinner wire will have higher resistance. See the separate Electric Resistivity Converter for that quantity.
Is volt/ampere the same thing as an ohm?
Yes — they're numerically and dimensionally identical. The ohm is simply the named SI unit for the quantity that Ohm's law defines as voltage divided by current, so 1 V/A always equals exactly 1 Ω.
Why is the statohm so much larger than the ohm?
The statohm comes from the CGS electrostatic (ESU) unit system, which was built directly from Coulomb's law rather than the ampere-based definitions SI units use. The huge gap between the statohm and the ohm — roughly a factor of 9×10¹¹ — traces back to a conversion constant related to the speed of light that separates the electrostatic and electromagnetic CGS unit families.
What is quantized Hall resistance used for?
It's a fundamental resistance value, R_K = h/e², that appears as extremely precise, naturally quantized plateaus in the quantum Hall effect. Since 1990, national metrology institutes have used a fixed conventional value of this constant (25,812.807 ohms) as the international standard for calibrating precision resistance measurements, because it's far more reproducible than any physical resistor.